Question

Is this correct?
Let f(x,y) = 2x^2 + 2xy + 3y^2 - 16x - 18y +54

(a) Find f_x (x,y)

4x+2y-16

(b) Find f_y (x,y)

2x+6y-18

(c) Evaluate f_x (1,-2)

4(1)+2(-2)-16 = -16

(d) Evaluate f_y (1,2)

2(1)+6(2)-18=-4

Answer 1

again, every answer is correct

Answer 2

nice work

Answer 3

ok great wasn't sure I did it right. I get confused on the removing the y's and x's when they are right next to each other.

for example the 2xy that threw me for a loop.

Answer 4

you would just think of 2x as the constant if you were deriving with respect to y

Answer 5

or 2y as the constant if you were deriving with respect to x

Answer 6

ok I think I got it, was curious cause the 2xy is like saying (2)(x)(y) so I guess you just remove the x because it would be 2x which the derivative would just be 2 so the only things left are (2)(y). Is that right?

Answer 7

However, if it was 2x^2y it would be 4xy right?

Answer 8

yeah you can think of 2xy as 2yx = (2y)*x

derive that with respect to x to get (2y)*1= 2y

the 2y is being treated as a constant

Answer 9

what are you deriving 2x^2y with respect to?

Answer 10

x

Answer 11

yes you are correct

d/dx[2x^2y] = 4xy

Answer 12

ok sweet, dang man you are freaking smart. I wish I was that good.

Answer 13

just keep practicing it and you'll get it and master it in no time

Answer 14

and you seem like you know what you're doing here, which is great

Answer 15

Hope so I have to make an A in this class.

Answer 16

I'm sure you will

Answer 17

Thanks. I fanned you and would love to ask you questions when I have more. Talk to you later.

Answer 18

And thanks for everything.

Answer 19

alright, have a nice night